PSI - Issue 84

Vanni Nicoletti et al. / Procedia Structural Integrity 84 (2026) 638–644

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Fig. 2. Real cable-stayed bridge case study: (a) aerial photo; (b) schematic view with main geometric features.

Fig. 3. Results of the proposed OSP procedure: (a) choice of the number of monitored stays N ; (b) OF evolution; (c) position of load cells installed on the bridge for the SHM; (d) optimal position of load cells obtained by the method.

The PSO algorithm is implemented with a high number of iterations and strict convergence criteria to ensure accuracy, while maintaining limited computational cost by relying on precomputed finite element model results. As previously stated, equal weights are assigned to all coefficients in the objective function. After defining the number of target modes ( =7 ), a preliminary analysis is carried out to determine the optimal number of sensors by progressively reducing the number of monitored stays from 40 to 1. The evolution of the objective function and its coefficients ( Fig. 3a ) shows that, while increasing the number of sensors improves performance, benefits become negligible beyond eight stays. As a result, =8 is selected as the optimal number of monitored stays. The OSP procedure is then performed assuming =8 and =7 , leading to convergence after multiple PSO steps and confirming the computational efficiency of the approach. The final sensor layout ( Fig. 3d ) is well distributed along the bridge span and nearly symmetric, ensuring comprehensive structural monitoring. Compared to the original configuration— Fig. 3c designed primarily for static force monitoring and considering only c 1 coefficient—the optimized layout provides a more balanced distribution of sensors and enhances also the identification of the bridge’s dynamic behavior.